Accurate waveform measurements are desirable in a number of fields. An example is electrical measurements, for example impedance measurements. Generally, these types of measurements involve analysis of the signal in the frequency domain.
Traditionally, amplitude measurement using frequency analysis has required that the sample speed, analysed time, and signal frequency are adapted such that exactly an integer number of periods are analysed. This is called synchronised sampling. In this case, the signal frequency must always be known prior to the measurement, otherwise the estimated amplitude will receive an error that is dependent of the difference between the assumed frequency and the actual frequency of the signal.
In order to reduce the problems with synchronised sampling, interpolated Fast Fourier Transform (FFT) as disclosed in e.g. “High-Accuracy measurements via Interpolated FFT” by Jain et al., published in IEEE Transactions on Instruments and Measurements, Vol. Im-28, No. 2, June 1978, may be used. Here, usually two or a maximum of three frequency bins are used for the interpolation.
It is also known to use windows for harmonic analysis, as disclosed in “On the Use of Windows for Harmonic Analysis with Discrete Fourier Transform” by Harris, published in Proceedings of the IEEE, vol. 66, No. 1, January 1978, to detect harmonic signals in the presence of broad-band noise, and in the presence of nearby harmonic interference.
Among the measurements performed for testing and development of high-voltage equipment, dielectric response measurements are extreme in precision requirements. Modern insulation materials often have losses in the range 10−4 or less, whereas a precision of 10−2 is sufficient in most other electrical measurements.
To achieve high precision, most dielectric response techniques use a balancing circuit to suppress the dominating capacitive current. Traditionally, this is done in a bridge circuit where one bridge arm is adjusted to minimize the difference current. Balancing techniques require careful control and well-defined waveforms and are therefore impossible to perform on equipment in service.
Modern instrumentation technology has advanced so far that instrumentation for measurements with resolution as high as 10−6 is commercially available for frequency ranges up to 10 kHz and higher.
The paper “Straight Dielectric Response Measurements with High Precision”, by J. Hedberg and T. Bengtsson, Nord-IS 2005, paper 27, discloses a dielectric response instrument with high precision. According to this paper, the digital processing of the measurements made by the measurement circuit involve discrete Fourier transform of the measurement data in order to extract the frequency and complex amplitude in the peaks of the Fourier transformed data. It is further disclosed that it is advantageous to sample very long records to improve accuracy.